About me

My name is Trinh Tuan Phong. I have just finished my Ph.D. thesis under the supervision of Prof. Frédéric Klopp, IMJ, Paris 6, on random and periodic Schrödinger operators.
My thesis consists of two parts: the random and periodic operators in dimension 1.
In the first part, we prove the decorrelation estimate for a 1D lattice Hamiltonian with off-diagonal disorder. Consequently, we deduce the asymptotic independence of the local level statistics near distinct positive energies in the localized regime. Finally, we revisit a known result on the decorrelation estimate for the 1D discrete Anderson model.
The second part of my thesis addresses questions on resonances for a 1D Schrödinger operators with truncated periodic potential. Precisely, we consider the half-line operator $H^{\mathbb N}=-\Delta +V$ and $H^{\mathbb N}_{L}= -\Delta + V\mathbbm{1}_{[0, L]}$ acting on $\ell^{2}(\mathbb N)$ with Dirichlet boundary condition at $0$. We describe the resonances of $H^{\mathbb N}_{L}$ near the boundary of the essential spectrum of $H^{\mathbb N}$ as $L \rightarrow +\infty$, hence complete the results introduced by my advisor in 2013 on the resonances of $H^{\mathbb N}_{L}$.
Here is the final version of my thesis.
My CV is available here.

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